er of Reaction GEORGE M. RIACHWART AND ROBERT E. QUILICI’ Michigan College of Mining and Technology, Houghton, Mich.
HEN repeated determinations of the order of homogeneous reactions are to be made, t h e use of a nomograph shortens the time required. T h e accompanying nomograph (Figure 1) was constructed using the theory ( 2 ) expressed in t h e following equations.
and
Reaction 2 results after the formation of X moles of product iyhen the concentration of the reactant is A - X. T h e exponential power on the A - X term or iV shows the order of reaction. When different values of concentration or A - X are used along with their corresponding rates, - d c / d T , a constancy of t h e calculated k value shows that the proper 4 value or reaction order has been used. T h e nomograph \T-as constructed using fixed locations for the A - X and k axes. T h e rate scales, which were locat’ed graphically, have different locations, depending on whether N has a value of I / * , 1, 2 , or 3. T h e nomograph has three parallel axes (1) and is of the general type r y = z. I n using the nomograph a curve of A - X against T (time) is necessary. Rates a t points on the curve are determined by means of the slope at, the point. An example of the chart use is in connection with the order of reaction (3)for the conversion of AT-chloroacetanilide into p-chloroacetanilide (see Figure 2 ) . T h e slope or rate at’ point P with a n A - X value of 42 is 3.3 X 10-3. Point &Ifon the curve with a n A - X T h e use of a mevalue of 30 has a rate value of 2.7 X chanical aid such as a tangimeter ( 4 ) facilit,ates the slope determination. On the nomograph point P is located on the A - X axis and a straight line is draivn from i t through the rate value of 3.3 X 10-3 on the N = 1 rate line until the line intersects the k line. This procedure is repeated for point T h e k value is 8 X 10-5. M , which gives a k value of 9 X 10-5. The intersection of these two lines a t or near the same k value shoi7-s t h a t the N value chosen is correct and the reaction is of the first order. Other lines drawn from t h e same A - X point through other rate axes show a wide divergence.
T , T I M E IN SECONDS Figure 2. Example of use of nomograph for conversion of N-chloroacetanilide into p-chloroacetanilide
LITERATURE CITED
Davis, D. S.,”Empirical Equations and Somographs,” p. 104, McGraw-Hill, New York, 1943. ( 2 ) Laidler, X. J., “Chemical Kinetics,” p. 5 , hIcGraw-Hill, S e w York, 1950. (1)
(3) I b i d . , p. 6. (4) Simons, H. P., IXD.ENG.CHEX.,ANAL. ED. 13, 663 (1941).
RECEIVED for review J u l y 27, 1955.
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Present address, United States Air Force.
ACCEPTED J a n u a r y 24, 1956.
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1956
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Figure 1.
Nomograph for determining order of homogeneous reaction
